Nuprl Lemma : no-descending-chain_wf
∀[T:Type]. ∀[<:T ⟶ T ⟶ ℙ]. (no-descending-chain(T;<) ∈ ℙ)
Proof
Definitions occuring in Statement :
no-descending-chain: no-descending-chain(T;<),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
no-descending-chain: no-descending-chain(T;<),
so_lambda: λ2x.t[x],
nat: ℕ,
prop: ℙ,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
so_apply: x[s]
Lemmas referenced :
all_wf,
nat_wf,
exists_wf,
int_seg_wf,
not_wf,
infix_ap_wf,
int_seg_subtype_nat,
false_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
hypothesis,
cumulativity,
hypothesisEquality,
lambdaEquality,
because_Cache,
natural_numberEquality,
setElimination,
rename,
instantiate,
universeEquality,
applyEquality,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[T:Type]. \mforall{}[<:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. (no-descending-chain(T;<) \mmember{} \mBbbP{})
Date html generated:
2016_05_13-PM-03_52_04
Last ObjectModification:
2015_12_26-AM-10_17_00
Theory : bar-induction
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